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Topic: Matheology � 263
Replies: 57   Last Post: May 17, 2013 8:52 PM

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 263
Posted: May 14, 2013 2:46 AM

In article
Graham Cooper <grahamcooper7@gmail.com> wrote:

> On May 14, 1:36 pm, Virgil <vir...@ligriv.com> wrote:
> > In article
> >  Graham Cooper <grahamcoop...@gmail.com> wrote:
> >

> > > On May 14, 11:09 am, Virgil <vir...@ligriv.com> wrote:
> > > > In article
> > > > Graham Cooper <grahamcoop...@gmail.com> wrote:

> >
> > > > > such as Virgil's favorite number!
> >
> > > > > 0.44444454444444444445444444545544444444445444444444444...
> >
> > > > That denotes, as yet, any of a range of real numbers, not any specific
> > > > one, and whichever ones in that range Graham finds his favorite, none of
> > > > them are anything like my favorite.

> >
> > > Real numbers of that form are all you need to show
> >
> > I don't need to show any any such numbers.
> >
> >
> >

> > > | POINTS |  >  | INFINITE LIST |
> >
> > > between these 2 bars!
> >
> > > --->|----|<----
> >
> > > Here's another one
> >
> > > 0.4444444444445444444444454444445444444444454444445444444...
> >
> > > Remember your hero CANTOR showed you how to CONSTRUCT that number!
> >
> > > You post 20 times a day the Algorithm (sic) to construct that real!
> >
> > The algorithm I regularly post, and Cantor first used, is for binary
> > sequences not decimals.
> >
> > Neither type of "antidiagonal" is defined without an infinite list of
> > sequences of the the appropriate type from which to build it, which
> > lists you have not provided, so no anti-diagonal need exist until you do.
> >

>
> Such algorithms have been posted 100 times.
>
> Though You have no clue what Cantor's Missing Set function actually
> does.
>
>
> SET1 = { 1 , 3 , 6 }
> SET2 = { 1 , 5 , 11 }
> SET3 = { 2 , 4 , 6, 8 , 10 , ... }
> SET4 = { 4 , 5, 6, 7, 8 }
>
> [VIRGIL]
>
> Given an arbitrary function f from |N to the powerset of |N (set of
> all subsets of |N), the set S = {n in |N | ~ n in f(n)} is a subset of
> |N not in the image of f, and thus is a proper "Cantor's missing
> set".
>
> You learnt this magic formula off by heart and you have no idea how to
> apply it!

I have learnt the quadratic formula off by heart, too, though, at need I
can derive it from the quadratic equation, a*x^2 + b*x + c = 0, and
apply it.
>
> and the Missing Set from the above enumeration is.... ?

In order to be able to use the definition "S = {n in |N | ~ n in f(n)}"
and thus determine which sets are missing in the image of a given
function, f: |N --> 2^|N, one must first be able to determine all the
values of that function, i.e., one subset of |N for each member of |N..

If you only give me

f(1) = { 1 , 3 , 6 }
f(2) = { 1 , 5 , 11 }
f(3) = { 2 , 4 , 6, 8 , 10 , ... }
f(4) = { 4 , 5, 6, 7, 8 }

All I know so far is that that your f cannot be such a function
because 1 is in f(1) and 4 is in f(4).
--

Date Subject Author
5/10/13 Virgil
5/13/13 Virgil
5/13/13 Graham Cooper
5/13/13 Virgil
5/13/13 Graham Cooper
5/13/13 Virgil
5/14/13 Graham Cooper
5/14/13 Virgil
5/14/13 Graham Cooper
5/14/13 Virgil
5/14/13 Graham Cooper
5/14/13 Virgil
5/14/13 Graham Cooper
5/14/13 Virgil
5/14/13 Graham Cooper
5/14/13 Virgil
5/15/13 Graham Cooper
5/15/13 Virgil
5/15/13 Graham Cooper
5/15/13 Virgil
5/15/13 Graham Cooper
5/15/13 Virgil
5/15/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Scott Berg
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Virgil
5/16/13 Graham Cooper
5/17/13 Virgil
5/17/13 Graham Cooper
5/17/13 Virgil
5/17/13 Graham Cooper
5/17/13 Virgil
5/17/13 Graham Cooper
5/17/13 Virgil
5/17/13 Graham Cooper
5/14/13 Graham Cooper
5/14/13 Virgil